Optical system, and image observing apparatus and image pickup apparatus using it

ABSTRACT

The present invention relates to an optical system apparatus, which has a first surface symmetric with respect to only one symmetry plane and a second surface symmetric with respect to only the symmetry plane, in which the first plane is a reflective, concave surface and is inclined relative to a reference axial ray present in the symmetry plane. Further, a local power of the second surface changes from a positive to a negative.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an optical system, and moreparticularly, to an optical system suitable for applications in imageobserving apparatuses such as a finder of a camera and a so-calledhead-mounted display, and in image pickup apparatuses such as cameras.

2. Related Background Art

For the head-mounted display, a variety of optical systems have beendevised heretofore in order to compactify the entire apparatus.

For example, Japanese Laid-open Patent Application No. 58-78116discloses an optical apparatus for observing an object image on aprimary image plane, obtained by a photographing optical system, throughan optical element in a prism shape having a concave, spherical,reflecting surface set as inclined to the observer's eye.

Since the reflecting surface is an inclined spherical surface in thisconventional example, it is difficult to correct well for opticalaberrations including astigmatism, occurring there. The official gazetteof the above application describes a need to add a new lens system forimproving correction for the aberrations.

Japanese Laid-open Patent Application No. 5-303055 discloses an opticalsystem having an additional lens system (relay lens system) of thistype. Addition of such a relay lens system, however, lengthens the totallength of the optical system, resulting in a defect of spoilingcompactification of the optical system.

Japanese Laid-open Patent Applications No. 5-303054, No. 5-303056, andNo. 5-323229 disclose optical systems in which one reflecting surfaceout of the following surfaces is inclined relative to the optical axisof the observer's eye in order to improve compactification andaberrations of optical system: normal aspherical surfaces of revolutionhaving high-order aspherical terms; paraboloids and ellipsoids ofrevolution given by conical functions, each defined by a conicalcoefficient; toric aspherical surfaces (or anamorphic asphericalsurfaces), each expressed by mutually different aspherical functions onorthogonal coordinate axes.

These optical systems, however, need to be corrected for distortion,curvature of field, and focus difference in orthogonal directions (i.e.,astigmatism). A desired method for focusing (diopter adjustment) of theso-called decentering optical system with the inclined reflectingsurface is to move the focal plane of the optical system (an imagedisplay device or an image pickup device), because moving the opticalsystem causes a great change of optical performance. To realize it, adesired optical system is telecentric with respect to the focal plane.

Checking the above conventional examples from this viewpoint, theoptical system in Japanese Laid-open Patent Application No. 5-303054 iscorrected for curvature of field and distortion, but still hasastigmatism left without being corrected for.

The optical system in Japanese Laid-open Patent Application No. 5-303056is corrected for astigmatism and distortion, but still has curvature offield left without being corrected for.

Further, the optical system in Japanese Laid-open Patent Application No.5-323229 is corrected for curvature of field, astigmatism, anddistortion, but it has angles of rays largely inclined relative to thefocal plane, which, in the case of a display device such as a liquidcrystal panel or an image pickup device such as a CCD being located onthe focal plane, causes a defect of greatly degrading the performancebecause of an angle dependence of characteristics of the device.

Although the optical systems proposed in the above applications arecorrected for distortion, distortion is recognized at a glance, andcorrection for distortion is thus inadequate.

As described above, the arrangements with a single, aspherical,reflecting surface had the defect that all the aberrations were unableto be adequately corrected for.

Japanese Laid-open Patent Application No. 3-180810 discloses increasingthe F-number for the optical system by setting the view point ofobserver away and arranging the optical system in such a manner thatcurvature of field and astigmatism are corrected by increasing the depthof focus of the optical system and that distortion distortion iscorrected by an aspherical surface having a cross term (e.g., xy) in theorthogonal coordinate system (x, y, z).

Since this optical system is based on the method for observing an imagefrom the view point set away, it does not permit, however, wider-anglearrangement or larger-screen arrangement. Although the optical systemwas arranged in the telephoto type in combination of a convex mirrorwith a concave mirror, it had a defect of the large size as a wholeagainst compactification.

SUMMARY OF THE INVENTION

An object of the present invention is to provide an optical systemformed in a very simple arrangement and well corrected for the variousaberrations.

An optical system of the present invention has a first surface and asecond surface, each surface being symmetric with respect to only onesymmetry plane, wherein the first surface is a reflecting concavesurface, which is inclined to a reference axial ray present in thesymmetry plane, and wherein a local power of the second surface changesfrom a positive to a negative.

In one embodiment of the optical system of the present invention, thelocal power of the second surface as to rays in the symmetry planeand/or the local power of the second surface as to rays in a plane beingperpendicular to the symmetry plane and including the reference axialray and in a plane parallel to the foregoing plane changes from apositive to a negative along a cut line where the symmetry plane cutsthe second surface.

In the optical system of the present invention, the local power of thesecond surface preferably changes from a positive to a negative alongthe cut line in a direction of from a shorter optical pathlength to alonger optical pathlength between the first surface and the secondsurface.

An image observing apparatus and an image pickup apparatus of thepresent invention are characterized by using the optical system of thepresent invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing to illustrate the optical action of the presentinvention;

FIG. 2 is a drawing to illustrate the optical action of the presentinvention;

FIGS. 3A and 3B are schematic drawings to show the major part ofEmbodiment 1 of the image observing apparatus according to the presentinvention;

FIGS. 4A to 4D are aberration diagrams to show aberrations of theoptical system in Embodiment 1;

FIG. 5 is a drawing to show distortion by the optical system ofEmbodiment 1;

FIG. 6 is a schematic drawing to show the major part of Embodiment 2 ofthe image observing apparatus according to the present invention;

FIGS. 7A to 7D are aberration diagrams to show aberrations of theoptical system in Embodiment 2;

FIG. 8 is a drawing to show distortion by the optical system ofEmbodiment 2;

FIG. 9 is a schematic drawing to show the major part of Embodiment 3 ofthe image observing apparatus according to the present invention;

FIGS. 10A to 10D are aberration diagrams to show aberrations of theoptical system in Embodiment 3;

FIG. 11 is a drawing to show distortion by the optical system ofEmbodiment 3;

FIG. 12 is a schematic drawing to show the major part of Embodiment 4 ofthe image observing apparatus according to the present invention;

FIGS. 13A to 13D are aberration diagrams to show aberrations of theoptical system in Embodiment 4;

FIG. 14 is a drawing to show distortion by the optical system ofEmbodiment 4;

FIG. 15 is a schematic drawing to show the major part of Embodiment 5 ofthe image observing apparatus according to the present invention;

FIGS. 16A to 16D are aberration diagrams to show aberrations of theoptical system in Embodiment 5;

FIG. 17 is a drawing to show distortion by the optical system ofEmbodiment 5;

FIG. 18 is an explanatory drawing of an absolute coordinate system andlocal coordinate systems employed in each embodiment;

FIGS. 19A and 19B are explanatory drawings of local radii of curvaturer_(Lx) and r_(Ly) ; and

FIGS. 20A and 20B are schematic drawings to show the major part of theimage pickup apparatus of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The optical action of the fundamental arrangement of the optical systemaccording to the present invention is first explained referring to FIG.1 and FIG. 2. In the drawings, S represents a stop, S1 a firstreflecting surface (optically acting surface), S2 a second reflectingsurface (optically acting surface), and P is a focal plane. Although inthe following description the optical system is explained as a system inwhich light originates from the stop S side to reach the focal plane P,for convenience's sake, the optical system, when applied to an actualimage observing optical system, is arranged as a system in which thelight originates from the focal plane P (image display device) to beincident to the stop S (the pupil of observer).

In the optical system of FIGS. 1 and 2, let us define a reference axialray Lo as a ray emerging from the center of the stop S and impinging onthe center P_(o) of the focal plane P nearly normally thereto. Further,principal rays L are rays emerging from the center of the stop S andimpinging upon respective points on the focal plane P nearly normallythereto.

As shown in FIG. 1, the first reflecting surface S1 is determined insuch a shape that the principal rays L from the stop S becomeapproximately telecentric toward the image side after reflected by thefirst reflecting surface S1 and that an average image plane is nearlysuperimposed on a plane H perpendicular to the reference axial ray Lo.

Here, considering light beams originating from an object at almostinfinity and passing the stop S in a cross section being parallel to theplane of the drawing and including the reference axial ray Lo (the Y-Zcross section as detailed later) and in a cross section beingperpendicular to the plane of the drawing and including the referenceaxial ray Lo (the X-Z cross section as detailed later), the averageimage plane is a plane including intermediate points between imagepositions of the rays in the respective cross sections. In FIG. 1, in alight beam at a certain field angle, points Me are image points of therays in the Y-Z cross section, and points Sa are image points of therays in the X-Z cross section. In this case middle points Q between thepoints Me and the points Sa in the principal rays L are points on theaverage image plane, and differences between the points Me and thepoints Sa are astigmatism. Telecentricity of principal rays anddistortion are affected by the total shape of reflecting surface, and animaging state of each beam (curvature of field, astigmatism) is affectedby the local shape of surface.

As explained in the description of the conventional examples, it isdifficult to achieve correction for these aberrations by a singlereflecting surface. In the present invention, therefore, the firstreflecting surface S1 is mainly arranged to maintain telecentricity ofprincipal rays and correct for distortion and to align the average imageplane with the plane H, and the second reflecting surface S2 correctsfor remaining astigmatism.

The second reflecting surface S2 is formed in such a shape as to mainlycorrect for astigmatism of the beam, as shown in FIG. 2. Specifically,the shape can be determined in such a manner that local imagemagnifications of rays in the Y-Z cross section increase from the nearside (A) with respect to the first reflecting surface S1 toward the farside (B) and that local image magnifications of rays in the X-Z crosssection decrease from the near side (A) with respect to the firstreflecting surface toward the far side (B). A magnification of a localsurface is a ratio b"/b' of an image distance b" to an object distanceb' of the outstanding surface, as shown in FIG. 2.

The second reflecting surface S2 is formed in such a shape that in theY-Z cross section from the near side (A) to the first reflecting surfacetoward the far side (B) the local power (ρ_(L) =-2N/r_(L)) changes froma positive to a strong negative and that in the X-Z cross section fromthe near side (A) to the first reflecting surface toward the far side(B) the local power changes from a positive or a weak negative to astrong negative.

The two reflecting surfaces having the shapes as described herein cancorrect for distortion, curvature of field, and astigmatism and maintaintelecentricity. If a third optically acting surface S3 (not shown) isplaced near the focal plane between the second reflecting surface S2 andthe focal plane P, the optical system can be corrected for slightdistortion and deviation of telecentricity caused by the shape of thesecond reflecting surface S2, thus further improving partial changes ofthe image plane.

The third optically acting surface S3 may be either a refracting surfaceor a reflecting surface. When the third optically acting surface S3 isprovided near the focal plane P, it can decrease overlap of beamsreaching the respective points (image points) on the focal plane P andit enables partial correction of image points by a partial change ofshape of surface, thereby readily correcting for aberrations that thefirst reflecting surface S1 and the second reflecting surface S2 asdescribed above fail to correct for.

Further, if the first reflecting surface S1, the second reflectingsurface S2, and the third optically acting surface S3 are formed on amedium such as glass or plastics, the optical system of the presentinvention can be realized by a single optical element, which is veryadvantageous in compactification and reduction of cost.

FIGS. 3A and 3B are schematic drawings to show the major part ofEmbodiment 1 of the image observing apparatus according to the presentinvention. In the drawings, B1 is an optical element, which has thefirst, the second, and the third optically acting surfaces S1, S2, S3.Each of the three acting surfaces is formed in a shape symmetric withrespect to only one plane (the YZ plane). S represents a desired pupilposition of the observer, and P a display surface of an image displaydevice.

The third optically acting surface S3 is shaped in an aspherical surfacesymmetric with respect to only the symmetry plane, and is located nearlyperpendicular to the reference axial ray Lo emerging from the center ofthe display surface P nearly normally to the display surface P. Thesecond optically acting surface S2 is shaped in an aspherical surfacesymmetric with respect to only the symmetry plane, and is located asinclined at such an angle as to totally reflect the reference axial rayLo refracted by the third optically acting surface S3. The firstoptically acting surface S1 is an aspherical reflecting surface(obtained by depositing a reflecting film on a surface) of a totallystrong concave surface which is symmetric with respect to only thesymmetry plane, and is located as inclined relative to the referenceaxial ray Lo totally reflected by the second optically acting surfaceS2. The reference axial ray Lo reflected by the first optically actingsurface S1 passes through the second optically acting surface S2 toreach the pupil S.

The optical action of the present embodiment is next explained. A lightbeam emerging from an image displayed on the display surface P firsttravels through the third optically acting surface S3 toward the secondoptically acting surface S2 and is then totally reflected by the surfaceS2 toward the first optically acting surface S1. Then the beam isreflected by the surface S1 to become a converging beam, and the beamtravels again to the second optically acting surface S2. The beam passesthrough this surface S2 this time to form a virtual image of the imageand to reach the observer's pupil S, whereby the observer can visuallyrecognize the virtual image.

Since the optical system of the present embodiment is composed of thedecentering surfaces, an absolute coordinate system and local coordinatesystems are set in order to express the shape of the optical system.FIG. 18 is an explanatory drawing of the absolute coordinate system andlocal coordinate systems. This is next explained.

The origin of the absolute coordinate system is set at the center O ofthe desired pupil position S of observer, and the Z-axis is a straightline perpendicular to the pupil plane through the point O, as located onthe symmetry plane. The Y-axis is a straight line making an angle of 90°counterclockwise relative to the Z-axis on the symmetry plane andthrough the origin O. The X-axis is a straight line perpendicular to theY- and Z-axes through the origin O. The Z-axis is superimposed on thereference axial ray Lo coming from the center of the display surface Pof the image display device nearly normally to the display surface P toreach the center of the pupil S.

The origin Oi of each local coordinate system is set at absolutecoordinates (SXi, SYi, SZi). The z-axis of each local coordinate systemis a straight line passing through the origin Oi in the YZ plane andmaking an angle Ai with the Z-axis of the absolute coordinate system.The y-axis is a straight line passing through the origin Oi and makingan angle of 90° counterclockwise relative to the z-axis on the symmetryplane. The x-axis is a straight line passing through the origin Oi andbeing perpendicular to the y-axis and the z-axis.

The shape of each surface is expressed by local coordinates. Each of theshapes of the optically acting surfaces in each embodiment of thepresent invention is a shape as defined by the following function,having a conical function defined by the conical coefficient, andZernike polynomials. ##EQU1## In the above equation, c is the curvatureas defined by c=1/r, where r is a fundamental radius of curvature ofeach surface.

Further, k is the conical coefficient of each surface, and c_(j) is anaspherical coefficient of the j-th Zernike polynomial in each surface.

Table 1 shows data for the arrangement of Embodiment 1. In the table, fis a value corresponding to the focal length of the optical element B1,which is calculated by the following equation:

    f=y.sub.m /tan (θ)

where θ is an angle of incidence of incident light from an object atinfinity and y_(m) is a height of an image formed from rays of theincident light on the display surface P, and which is referred to simplyas focal length herein.

                  TABLE 1                                                         ______________________________________                                        f = 25   N = 1.4917                                                           Surface S1         S2         S3       P                                      ______________________________________                                        1/r     -1.300e-02 -3.019e-03 1.000e-18                                       k       3.357e+00  2.893e+01  0.000e+00                                       c.sub.1 -1.140e-03 3.475e-03  -7.305e-03                                      c.sub.2 1.230e-04  7.479e-04  -7.869e-03                                      c.sub.3 -1.090e-05 -6.391e-06 -6.117e-05                                      c.sub.4 -4.055e-05 -1.239e-04 -1.321e-04                                      c.sub.5 -1.380e-06 -8.946e-07 -3.732e-05                                      c.sub.6 -5.544e-08 -8.408e-08 1.586e-05                                       c.sub.7 -7.316e-08 -1.282e-08 -3.997e-06                                      c.sub.8 4.901e-09  -4.941e-09 3.691e-07                                       c.sub.9 -1.070e-09 -1.295e-08 -6.127e-07                                      c.sub.10                                                                              1.202e-08  -2.201e-08 4.124e-07                                       SX      0.00       0.00       0.00     0.00                                                                          (mm)                                   SY      -9.03      -20.56     19.26    26.08                                                                         (mm)                                   SZ      23.92      20.53      29.43    30.17                                                                         (mm)                                   A       -30.70     0.29       54.37    50.00                                                                         (deg)                                  ______________________________________                                    

Table 2 includes local radii of curvature and r_(Ly) of the secondoptically acting surface S2 as expressed at six points on the actingsurface. Coordinates in the table are local coordinates of the surface.

                  TABLE 2                                                         ______________________________________                                                    x                                                                 y             0        8.01                                                   ______________________________________                                        r.sub.Lx (mm)                                                                 19.28         372.15   126.63                                                 31.57         119.31   55.94                                                  43.87         99.74    43.92                                                  r.sub.Ly (mm)                                                                 19.28         -1221.59 -725.14                                                31.57         1295.43  3372.99                                                43.87         87.94    89.32                                                  ______________________________________                                    

The local radii of curvature r_(Lx) and r_(Ly) are next explained. FIGS.19A and 19B are explanatory drawings of the local radii of curvaturer_(Lx) and r_(Ly).

The local radius of curvature r_(Lx) is a local radius of curvature onan intersecting line between the surface Si and a plane parallel to thex-z plane (which is y=y_(T) away in the drawing), as shown in FIG. 19A.

Further, the local radius of curvature r_(Ly) is a local radius ofcurvature on an intersecting line between the surface Si and a planeparallel to the y-z plane (which is x=x_(T) away in the drawing), asshown in FIG. 19B. Here, the local radius of curvature r_(Lx) or r_(Ly)takes a negative value when the optically acting surface is concave onthe light incidence side.

A local optical power ρ_(Lx) on the x-z plane is obtained from thefollowing equation:

    ρ.sub.Lx =-2N/r.sub.Lx

with the local radius of curvature r_(Lx) and a refractive index N of amedium in which the light travels.

Further, a local optical power ρ_(Ly) of the y-z plane is obtained fromthe following equation:

    ρ.sub.Ly =-2N/r.sub.Ly

with the local radius of curvature r_(Ly) and the refractive index N ofthe medium in which the light travels.

FIGS. 4A to 4D are aberration diagrams of Embodiment 1. The aberrationdiagrams indicate lateral aberrations at the image point on thereference axial ray Lo, the image points of ±ω in the y-direction to thereference axial ray Lo, and the image point of +η in the x-directionrelative to the reference axial ray Lo.

FIG. 5 shows distortion of an image of a grid object when ray trace fromthe pupil S to the display surface P is carried out in the imageobserving apparatus of the present embodiment. Supposing distortion ofthe image on the display surface P is pincushion distortion and if theray trace is carried out from the display surface P to the pupil S forthe optical system, distortion of image becomes of a barrel form in anopposite shape.

FIG. 6 is a schematic drawing to show the major part of Embodiment 2 ofthe image observing apparatus according to the present invention. Thepresent embodiment has a shorter focal length of the total system thanEmbodiment 1 has, thereby achieving a wider-angle arrangement. Table 3shows data for the arrangement of Embodiment 2.

                  TABLE 3                                                         ______________________________________                                        f = 20.5   N = 1.4917                                                         Surface S1         S2         S3       P                                      ______________________________________                                        1/r     -1.197e-02 -3.098e-03 1.000e-18                                       k       3.638e+00  5.894e+01  0.000e+00                                       c.sub.1 -2.424e-03 6.045e-04  -3.577e-03                                      c.sub.2 1.241e-03  1.703e-03  -1.144e-02                                      c.sub.3 -5.818e-05 -1.654e-05 9.935e-05                                       c.sub.4 -1.016e-04 -1.183e-04 5.979e-04                                       c.sub.5 -2.822e-06 -3.624e-07 -5.158e-06                                      c.sub.6 -8.333e-08 1.161e-07  -1.996e-05                                      c.sub.7 1.132e-07  -1.273e-07 1.104e-05                                       c.sub.8 3.918e-09  -4.273e-09 3.470e-07                                       c.sub.9 -3.311e-09 -1.754e-08 -1.034e-06                                      c.sub.10                                                                              2.136e-08  -3.668e-08 3.706e-07                                       SX      0.00       0.00       0.00     0.00                                                                          (mm)                                   SY      -13.79     -14.41     20.87    22.97                                                                         (mm)                                   SZ      16.11      17.12      21.72    28.24                                                                         (mm)                                   A       -33.64     2.95       63.43    44.00                                                                         (deg)                                  ______________________________________                                    

Table 4 includes the local radii of curvature r_(L) of the secondoptically acting surface S2 of the present embodiment at six points onthe acting surface.

                  TABLE 4                                                         ______________________________________                                                    x                                                                 y             0        7.43                                                   ______________________________________                                        r.sub.Lx (mm)                                                                 13.09         194.78   100.45                                                 24.36         85.73    50.16                                                  35.62         64.39    34.95                                                  r.sub.Ly (mm)                                                                 13.09         -224.21  -203.66                                                24.36         -1105.56 -632.99                                                35.62         53.99    47.78                                                  ______________________________________                                    

FIGS. 7A, 7B, 7C, and 7D are aberration diagrams of Embodiment 2. Theaberration diagrams indicate lateral aberrations at the image point onthe reference axial ray Lo, the image points of ±ω in the y-directionrelative to the reference axial ray Lo, and the image point of +η in thex-direction relative to the reference axial ray Lo.

Further, FIG. 8 shows distortion of an image of the grid object when theray trace is carried out from the pupil S to the display surface P inthe present embodiment.

FIG. 9 is a schematic drawing to show the major part of Embodiment 3 ofthe present invention. The present embodiment has a higher refractiveindex of the optical element B1 than Embodiment 1 has. Table 5 showsdata for the arrangement of Embodiment 3.

                  TABLE 5                                                         ______________________________________                                        f = 25   N = 1.5709                                                           Surface S1         S2         S3       P                                      ______________________________________                                        1/r     -1.425e-02 -3.458e-03 -3.816e+05                                      k       2.081e+00  3.740e+01  -4.349e+19                                      c.sub.1 -1.552e-03 -2.223e-03 3.382e-02                                       c.sub.2 -1.688e-05 7.360e-04  -2.115e-02                                      c.sub.3 -1.525e-05 -1.120e-06 -9.858e-04                                      c.sub.4 5.912e-06  -7.827e-06 1.271e-03                                       c.sub.5 2.190e-07  2.515e-07  -2.113e-05                                      c.sub.6 -2.240e-09 5.836e-08  6.744e-06                                       c.sub.7 2.052e-07  6.531e-09  -4.684e-06                                      c.sub.8 0.000e+00  0.000e+00  0.000e+00                                       c.sub.9 0.000e+00  0.000e+00  0.000e+00                                       c.sub.10                                                                              0.000e+00  0.000e+00  0.000e+00                                       SX      0.00       0.00       0.00     0.00                                                                          (mm)                                   SY      4.52       -17.48     23.49    25.16                                                                         (mm)                                   SZ      29.86      22.56      13.32    30.00                                                                         (mm)                                   A       -17.14     12.02      93.16    47.74                                                                         (deg)                                  ______________________________________                                    

Table 6 includes the local radii of curvature r_(L) of the secondoptically acting surface S2 of the present embodiment at six points onthe acting surface.

                  TABLE 6                                                         ______________________________________                                                    x                                                                 y             0        7.956                                                  ______________________________________                                        r.sub.Lx (mm)                                                                 15.822        148.28   153.68                                                 27.607        105.77   107.73                                                 39.393        68.94    61.94                                                  r.sub.Ly (mm)                                                                 15.822        -262.35  -281.74                                                27.607        -493.24  -627.27                                                39.393        78.11    61.94                                                  ______________________________________                                    

FIGS. 10A, 10B, 10C, and 10D are aberration diagrams of Embodiment 3.The aberration diagrams indicate lateral aberrations at the image pointon the reference axial ray Lo, the image points of ±ω in the y-directionrelative to the reference axial ray Lo, and the image point of +η in thex-direction relative to the reference axial ray Lo.

Further, FIG. 11 shows distortion of an image of the grid object whenthe ray trace is carried out from the pupil S to the display surface Pin Embodiment 3.

FIG. 12 is a schematic drawing to show the major part of Embodiment 4 ofthe image observing apparatus of the present invention. The presentembodiment is a so-called anamorphic optical system in which the focallength fx in the z-x plane is set to be different from the focal lengthfy in the z-y plane. Table 7 shows data for the arrangement of thepresent embodiment.

                  TABLE 7                                                         ______________________________________                                        fx = 18.9  fy = 25  N = 1.4917                                                Surface S1         S2         S3       P                                      ______________________________________                                        1/r     -1.365e-02 -3.666e-03 1.000e-18                                       k       2.536e+00  4.900e+01  0.000e+00                                       c.sub.1 -1.680e-03 -6.306e-04 -1.937e-02                                      c.sub.2 -5.361e-05 7.103e-04  -9.103e-03                                      c.sub.3 -1.661e-05 -1.425e-05 -6.073e-04                                      c.sub.4 -3.827e-05 -5.428e-05 8.702e-04                                       c.sub.5 -8.021e-07 4.539e-07  -1.450e-05                                      c.sub.6 7.894e-07  3.904e-07  9.317e-06                                       c.sub.7 2.509e-07  2.408e-07  3.628e-06                                       c.sub.8 3.169e-09  -2.739e-09 3.961e-07                                       c.sub.9 -7.055e-09 -4.684e-09 -6.382e-07                                      c.sub.10                                                                              4.031e-09  -2.042e-08 -1.100e-07                                      SX      0.00       0.00       0.00     0.00                                                                          (mm)                                   SY      -13.43     -13.71     19.27    23.92                                                                         (mm)                                   SZ      19.40      20.58      25.76    27.89                                                                         (mm)                                   A       -35.10     4.64       65.10    53.42                                                                         (deg)                                  ______________________________________                                    

Table 8 includes the local radii of curvature r_(L) of the secondoptically acting surface S2 of the present embodiment at six points onthe acting surface.

                  TABLE 8                                                         ______________________________________                                        r.sub.Lx ( mm)                                                                            x                                                                 y             0        9.29                                                   ______________________________________                                        11.49         150.81   172.70                                                 22.61         103.08   88.38                                                  33.74         86.24    53.95                                                  r.sub.Ly (mm)                                                                             x                                                                 y             0        7.43                                                   ______________________________________                                        11.49         -2089.76 -1052.29                                               22.61         208.58   242.14                                                 33.74         26.38    20.44                                                  ______________________________________                                    

FIGS. 13A, 13B, 13C, and 13D are aberration diagrams of Embodiment 4.The aberration diagrams indicate lateral aberrations at the image pointon the reference axial ray Lo, the image points of ±ω in the y-directionrelative to the reference axial ray Lo, and the image point of +η in thex-direction relative to the reference axial ray Lo.

Further, FIG. 14 shows distortion of an image of the grid object whenthe ray trace is carried out from the pupil S to the display surface Pin Embodiment 4. Since the focal length fx in the z-x plane is shorterthan the focal length fy in the z-y plane, a virtual image of the imagedisplayed on the display surface P is expanded 1.32 times larger in thex-direction than in the y-direction.

FIG. 15 is a schematic drawing to show the major part of Embodiment 5 ofthe image observing apparatus according to the present invention. Thepresent embodiment has an arrangement different from those of theprevious embodiments, and is arranged in such a manner that the opticalsystem is composed of a first member C1 and a second member C2, thefirst member C1 has a first reflecting surface (first optically actingsurface) S1 of an aspherical surface symmetric with respect to only onesymmetry plane, and the surface is set as inclined relative to thereference axial ray Lo. The second member C2 has a second reflectingsurface (second optically acting surface) S2 of an aspherical surfacesymmetric with respect to only the symmetry plane, and the surface isset as inclined relative to the reference axial ray Lo reflected by thefirst reflecting surface S1.

The action of the present embodiment is next explained. A light beamemerging from the image displayed on the display surface P of the imagedisplay device is reflected by the second reflecting surface S2 towardthe first reflecting surface S1. Then the light beam is reflected andconverged by this surface S1 to form an enlarged, virtual image of theimage and to be incident to the pupil S of observer, whereby theobserver can visually recognize the enlarged, virtual image of theimage. Table 9 shows data for the arrangement of the present embodiment.

                  TABLE 9                                                         ______________________________________                                        f =25                                                                         Surface    S1          S2          P                                          ______________________________________                                        1/r        -2.180e-02  9.607e-03                                              k          -2.403e+00  -8.765e+05                                             c.sub.1    -1.690e-03  -4.942e-03                                             c.sub.2    1.054e-04   -3.316e-03                                             c.sub.3    -3.020e-06  -7.399e-05                                             c.sub.4    -3.106e-05  -1.343e-04                                             c.sub.5    -2.921e-07  4.469e-06                                              c.sub.6    5.002e-07   1.861e-06                                              c.sub.7    1.721e-07   1.291e-06                                              c.sub.8    3.848e-09   -1.302e-08                                             c.sub.9    2.030e-08   -6.965e-08                                             c.sub.10   -7.029e-09  -1.790e-07                                             SX         0.00        0.00        0.00                                                                          (mm)                                       SY         9.24        18.35       16.43                                                                         (mm)                                       SZ         25.99       11.79       18.48                                                                         (mm)                                       A          -12.61      -7.75       26.96                                                                         (deg)                                      ______________________________________                                    

Table 10 indicates local powers of the second optically acting surfaceS2 of the present embodiment at six points on the acting surface.

                  TABLE 10                                                        ______________________________________                                                    x                                                                 y             0        5.70                                                   ______________________________________                                        r.sub.Lx (mm)                                                                 -12.51        69.99    -291.96                                                -6.66         61.71    307.96                                                 -0.8          47.92    73.34                                                  r.sub.Ly (mm)                                                                 -12.51        -94.08   -126.87                                                -6.66         -411.04  -1494.01                                               -0.8          345.00   277.42                                                 ______________________________________                                    

FIGS. 16A, 16B, 16C, and 16D are aberration diagrams of Embodiment 5.The aberration diagrams indicate lateral aberrations at the image pointon the reference axial ray Lo, the image points of ±ω in the y-directionrelative to the reference axial ray Lo, and the image point of +η in thex-direction relative to the reference axial ray Lo.

Further, FIG. 17 shows distortion of an image of the grid object whenthe ray trace is carried out from the pupil S to the display surface Pin Embodiment 5.

Thus, the present embodiment obtains the optical system arranged in aparticularly simple structure, which is well corrected for distortion,curvature of field, and astigmatism, and which almost satisfies thetelecentric condition to the display surface.

Each embodiment described above showed the optical system of the imageobserving apparatus, but an image pickup apparatus can also beconstructed by setting the stop S' at the position of the pupil S andsetting a recording surface of an image pickup means or a photoelectricconversion element R such as a CCD in place of the display surface P ofthe image display device, as shown in FIGS. 20A and 20B. Thisarrangement can achieve are image pickup apparatus well corrected forthe various aberrations and satisfying the telecentric condition to theimage pickup surface at a wide angle.

Since the arrangement of the optical element B1 in the presentembodiment is the same as in Embodiment 1, description thereof isomitted herein. It is, however, noted that the optical elements andoptical systems shown in Embodiments 2-5 can also be employed.

The present invention can achieve an optical system having a simplestructure and demonstrating good optical performance, based on the abovearrangements.

Particularly, if the first optically acting surface, the secondoptically acting surface, and the third optically acting surface areformed on a medium such as glass or plastics, the optical system can beconstructed in a single optical element, which permits ahigh-performance optical system to be manufactured at low cost.

What is claimed is:
 1. An optical system comprising, in an optical pathbetween a stop and a focal plane:a first surface symmetric with respectto only one symmetry plane; and a second surface symmetric with respectto only said symmetry plane, wherein said first surface is a reflective,concave surface and is inclined relative to a reference axial raypresent in said symmetry plane, wherein said reference axial ray is oneof (i) a ray which emerges from a center of the stop and isperpendicularly incident on a center of the focal plane and (ii) a raywhich emerges perpendicularly from the center of the focal plane and isincident on the center of the stop, and wherein said second surface isconfigured so that a power of a partial area of said second surfacechanges from positive to negative corresponding to respective locationsthereof.
 2. The optical system according to claim 1, wherein the powerof a partial area of said second surface as to rays in said symmetryplane changes from positive to negative along a cut line where saidsymmetry plane cuts said second surface.
 3. The optical system accordingto claim 2, wherein the power of a partial area of said second surfaceas to rays in said symmetry plane changes from positive to negative in adirection of from a shorter optical pathlength to a longer opticalpathlength between said first surface and second surface along said cutline.
 4. The optical system according to claim 2, wherein the power of apartial area of said second surface as to rays in the symmetry planecorrects for astigmatism occurring at said first surface.
 5. The opticalsystem according to claim 2, wherein the power of a partial area of saidsecond surface as to rays in a plane including said reference axial rayand being perpendicular to said symmetry plane and in a plane parallelto said plane changes from positive to negative along said cut line. 6.The optical system according to claim 5, wherein the power of a partialarea of said second surface as to the rays in the plane including saidreference axial ray and being perpendicular to said symmetry plane andin the plane parallel to said plane changes from positive to negative ina direction of from a shorter optical pathlength to a longer opticalpathlength between said first surface and second surface along said cutline.
 7. The optical system according to claim 5, wherein the power of apartial area of said second surface as to rays in said symmetry planeand the power of a partial area of said second surface as to the rays inthe plane including said reference axial ray and being perpendicular tosaid symmetry plane and in the plane parallel to said plane correct forastigmatism occurring at said first surface.
 8. The optical systemaccording to claim 2, wherein the power of a partial area of said secondsurface as to rays in a plane including said reference axial ray andbeing perpendicular to said symmetry plane and in a plane parallel tosaid plane changes from weak negative to strong negative along said cutline.
 9. The optical system according to claim 8, wherein the power of apartial area of said second surface as to the rays in the planeincluding said reference axial ray and being perpendicular to saidsymmetry plane and in the plane parallel to said plane changes from weaknegative to strong negative in a direction of from a shorter opticalpathlength to a longer optical pathlength between said first surface andsecond surface along said cut line.
 10. The optical system according toclaim 8, wherein the power of a partial area of said second surface asto rays in said symmetry plane and in a plane parallel to said symmetryplane and the power of a partial area of said second surface as to raysin the plane perpendicular to said symmetry plane and in the planeparallel to said plane correct for astigmatism occurring at said firstsurface.
 11. The optical system according to claim 1, wherein the powerof a partial area of said second surface as to rays in a plane includingsaid reference axial ray and being perpendicular to said symmetry planeand in a plane parallel to said plane changes from positive to negativealong a cut line where said symmetry plane cuts said second surface. 12.The optical system according to claim 11, wherein the power of a partialarea of said second surface as to the rays in the plane including saidreference axial ray and being perpendicular to said symmetry plane andin the plane parallel to said plane changes from positive to negative ina direction of from a shorter optical pathlength to a longer opticalpathlength between said first surface and second surface along said cutline.
 13. The optical system according to claim 11, wherein the power ofa partial area of said second surface as to the rays in the planeincluding said reference axial ray and being perpendicular to saidsymmetry plane and in the plane parallel to said plane corrects forastigmatism occurring at said first surface.
 14. The optical systemaccording to claim 1 further comprising a solid optical element which isprovided with said first surface and said second surface.
 15. An imageobserving apparatus comprising:image display means for displaying animage; and an optical system having a first surface and a second surfacesymmetric with respect to only one symmetry plane, wherein said secondsurface guides light from the image to said first surface, wherein saidfirst surface is a reflective, concave surface and is inclined relativeto a reference axial ray present in said symmetry plane, wherein saidreference axial ray is a ray which emerges perpendicularly from a centerof the image and is incident on a center of a stop, and wherein saidsecond surface is configured so that a power of a partial area of saidsecond surface changes from positive to negative corresponding torespective locations thereof.
 16. The image observing apparatusaccording to claim 15, wherein the power of a partial area of saidsecond surface as to rays in said symmetry plane changes from positiveto negative along a cut line where said symmetry plane cuts said secondsurface.
 17. The image observing apparatus according to claim 16,wherein the power of a partial area of said second surface as to rays insaid symmetry plane changes from positive to negative in a direction offrom a shorter optical pathlength to a longer optical pathlength betweensaid first surface and second surface along said cut line.
 18. The imageobserving apparatus according to claim 16, wherein the power of apartial area of said second surface as to rays in the symmetry planecorrects for astigmatism occurring at said first surface.
 19. The imageobserving apparatus according to claim 16, wherein the power of apartial area of said second surface as to rays in a plane including saidreference axial ray and being perpendicular to said symmetry plane andin a plane parallel to said plane changes from positive to negativealong said cut line.
 20. The image observing apparatus according toclaim 19, wherein the power of a partial area of said second surface asto the rays in the plane including said reference axial ray and beingperpendicular to said symmetry plane and in the plane parallel to saidplane changes from a positive to negative in direction of from a shorteroptical pathlength to a longer optical pathlength between said firstsurface and second surface along said cut line.
 21. The image observingapparatus according to claim 19, wherein the power of a partial area ofsaid second surface as to rays in said symmetry plane and the power of apartial area of said second surface as to the rays in the planeincluding said reference axial ray and being perpendicular to saidsymmetry plane and in the plane parallel to said plane correct forastigmatism occurring at said first surface.
 22. The image observingapparatus according to claim 16, wherein the power of a partial area ofsaid second surface as to rays in a plane including said reference axialray and being perpendicular to said symmetry plane and in a planeparallel to said plane changes from weak negative to strong negativealong said cut line.
 23. The image observing apparatus according toclaim 22, wherein the power of a partial area of said second surface asto the rays in the plane including said reference axial ray and beingperpendicular to said symmetry plane and in the plane parallel to saidplane changes from weak negative to strong negative in a direction offrom a shorter optical pathlength to a longer optical pathlength betweensaid first surface and second surface along said cut line.
 24. The imageobserving apparatus according to claim 22, wherein the power of apartial area of said second surface as to rays in said symmetry planeand the power of a partial area of said second surface as to rays in aplane including said reference axial ray and being perpendicular to saidsymmetry plane and in a plane parallel to said plane correct forastigmatism occurring at said first surface.
 25. The image observingapparatus according to claim 15, wherein the power of a partial area ofsaid second surface as to rays in a plane including said reference axialray and being perpendicular to said symmetry plane and in a planeparallel to said plane changes from positive to negative along a cutline where said symmetry plane cuts said second surface.
 26. The imageobserving apparatus according to claim 25, wherein the power of apartial area of said second surface as to the rays in the planeincluding said reference axial ray and being perpendicular to saidsymmetry plane and in the plane parallel to said plane changes frompositive to negative in a direction of from a shorter optical pathlengthto a longer optical pathlength between said first surface and secondsurface along said cut line.
 27. The image observing apparatus accordingto claim 25, wherein the power of a partial area of said second surfaceas to the rays in the plane including said reference axial ray and beingperpendicular to said symmetry plane and in the plane parallel to saidplane corrects for astigmatism occurring at said first surface.
 28. Theimage observing apparatus according to claim 15, wherein said opticalsystem has a third surface, andwherein the light from said image isincident to said third surface to be directed toward said secondsurface, then is reflected by said second surface toward said firstsurface, is converged and reflected by said first surface to be directedagain toward said second surface, and is emergent from said secondsurface toward an observer.
 29. The image observing apparatus accordingto claim 28, wherein said optical system is a prism having said first,second, and third surfaces.
 30. The image observing apparatus accordingto claim 15, wherein the stop comprises an observer's pupil.
 31. Animage pickup apparatus comprising:image pickup means for receiving lightfrom an object; and an optical system having a first surface and asecond surface symmetric with respect to only one symmetry plane,wherein said first surface guides the light from the object to saidsecond surface, wherein said first surface is a reflective, concavesurface and is inclined relative to a reference axial ray present insaid symmetry plane, wherein said reference axial ray is a ray whichemerges from a center of a stop and is perpendicularly incident on acenter of an image plane, and wherein said second surface is configuredso that a power of a partial area of said second surface changes frompositive to negative corresponding to respective locations thereof. 32.The image pickup apparatus according to claim 31, wherein the power of apartial area of said second surface as to rays in said symmetry planechanges from positive to negative along a cut line where said symmetryplane cuts said second surface.
 33. The image pickup apparatus accordingto claim 32, wherein the power of a partial area of said second surfaceas to the rays in said symmetry plane changes from positive to negativein a direction of from a shorter optical pathlength to a longer opticalpathlength between said first surface and second surface, along said cutline.
 34. The image pickup according to claim 32, wherein the power of apartial area of said second surface as to the rays in said symmetryplane corrects for astigmatism occurring at said first surface.
 35. Theimage pickup apparatus according to claim 32, wherein the power of apartial area of said second surface as to rays in a plane including saidreference axial ray and being perpendicular to said symmetry plane andin a plane parallel to said plane changes from positive to negativealong said cut line.
 36. The image pickup apparatus according to claim35, wherein the power of a partial area of said second surface as to therays in the plane including said reference axial ray and beingperpendicular to said symmetry plane and in the plane parallel to saidplane changes from positive to negative in a direction of from a shorteroptical pathlength to a longer optical pathlength between said firstsurface and second surface along said cut line.
 37. The image pickupapparatus according to claim 35, wherein the power of a partial area ofsaid second surface as to rays in said symmetry plane and the power of apartial area of said second surface as to the rays in the planeincluding said reference axial ray and being perpendicular to saidsymmetry plane and in the plane parallel to said plane corrects forastigmatism occurring at said first surface.
 38. The image pickupaccording to claim 32, wherein the power of a partial area of saidsecond surface as to rays in a plane including said reference axial rayand being perpendicular to said symmetry plane and in a plane parallelto said plane changes from weak negative to strong negative along saidcut line.
 39. The image pickup apparatus according to claim 38, whereinthe power of a partial area of said second surface as to the rays in theplane including said reference axial ray and being perpendicular to saidsymmetry plane and in the plane parallel to said plane changes from weaknegative to strong negative in a direction of from a shorter opticalpathlength to a longer optical pathlength between said first surface andsecond surface along said cut line.
 40. The image pickup apparatusaccording to claim 38, wherein the power of a partial area of saidsecond surface as to rays in said symmetry plane and the power of apartial area of said second surface as to rays in a plane including saidreference axial ray and being perpendicular to said symmetry plane andin a plane parallel to said plane correct for astigmatism occurring atsaid first surface.
 41. The image pickup apparatus according to claim31, wherein the power of a partial area of said second surface as torays in a plane including said reference axial ray and beingperpendicular to said symmetry plane and in a plane parallel to saidplane changes from positive to negative along a cut line where saidsymmetry plane cuts said second surface.
 42. The image pickup apparatusaccording to claim 41, wherein the power of a partial area of saidsecond surface as to the rays in the plane including said referenceaxial ray and being perpendicular to said symmetry plane and in theplane parallel to said plane changes from positive to negative in adirection of from a shorter optical pathlength to a longer opticalpathlength between said first surface and second surface along said cutline.
 43. The image pickup apparatus according to claim 41, wherein thepower of a partial area of said second surface as to the rays in theplane including said reference axial ray and being perpendicular to saidsymmetry plane and in the plane parallel to said plane corrects forastigmatism occurring at said first surface.
 44. The image pickupapparatus according to claim 31, wherein said optical system has a thirdsurface, andwherein the light from said object is incident to saidsecond surface to be directed toward said first surface, then isreflected by said first surface to be directed again to said secondsurface, is totally reflected by said second surface toward said thirdsurface, and is emergent from said third surface toward said imagepickup means.
 45. The image pickup apparatus according to claim 44,wherein said optical system is a prism having said first, second, andthird surfaces.
 46. The image pickup apparatus according to claim 31,wherein said optical system comprises a solid optical element which isprovided with said first surface and said second surface.
 47. An opticalsystem comprising, in an optical path between a stop and a focal plane:afirst surface symmetric with respect to only one symmetry plane; and asecond surface symmetric with respect to only said symmetry plane;wherein said first surface is a reflective, concave surface and isinclined relative to a reference axial ray present in said symmetryplane, wherein said reference axial ray is one of (i) a ray whichemerges from a center of the stop and is perpendicularly incident on acenter of the focal plane and (ii) a ray which emerges perpendicularlyfrom the center of the focal plane and is incident on the center of thestop, and wherein said second surface is configured so that a localpower ρ_(L), where ρ_(L) =-2N/r_(L), N is a refractive index of a mediumin which the light travels, and r_(L) is the local radius of curvatureat a location of said second surface, changes from positive to negativecorresponding to respective locations thereof.
 48. An image observingapparatus comprising:image display means for displaying an image; and anoptical system having a first surface and a second surface symmetricwith respect to only one symmetry plane, wherein said second surfaceguides light from the image to said first surface, wherein said firstsurface is a reflective, concave surface and is inclined relative to areference axial ray present in said symmetry plane, wherein saidreference axial ray is a ray which emerges perpendicularly from a centerof the image and is incident on a center of a stop, and wherein saidsecond surface is configured so that a local power ρ_(L), where ρ_(L)=-2N/r_(L), N is a refractive index of a medium in which the lighttravels, and r_(L) is the local radius of curvature at a location ofsaid second surface, changes from positive to negative corresponding torespective locations thereof.
 49. An image pickup apparatuscomprising:image pickup means for receiving light from an object; and anoptical system having a first surface and a second surface symmetricwith respect to only one symmetry plane, wherein said first surfaceguides the light from the object to said second surface, wherein saidfirst surface is a reflective, concave surface and is inclined relativeto a reference axial ray present in said symmetry plane, wherein saidreference axial ray is a ray which emerges from a center of a stop andis perpendicularly incident on a center of an image plane, and whereinsaid second surface is configured so that a local power ρ_(L), whereρ_(L) =-2N/r_(L), N is a refractive index of a medium in which the lighttravels, and r_(L) is the local radius of curvature at a location ofsaid second surface, changes from positive to negative corresponding torespective locations thereof.